This has come up a couple of times recently and there aren't a lot of tools out there for doing this easily but I came across a free, open source utility called DJV Imaging that I figured was worth a mention. The project is designed around viewing and manipulating image sequences in file formats common in the VFX world like OpenEXR and is available for Windows, Mac and Linux. It hasn't been updated in couple of years but hey, it worked for me!
This is the main GUI.
Importing a sequence is pretty self explanatory. Once imported you can use the transport controls to scrub through the sequence. You can even set in and out points if you want.
Under the File Menu there is an option to select the layer you want to view and work with. In this example there 3 layers, the beauty render, a diffuse layer and a Z depth layer.
If you select the Z depth layer you should see a grey scale depth map sequence.
Now you should be able to save just this layer as a separate sequence using the regular Save option under the file menu. Remember to add the .exr file extension to the file name.
P.S. Any errors or incoherence in this post should be blamed on Unibroue's La Fin Du Monde Tripel